Problem: $\int x^9\,dx=$ $+C$
The integrand is of the form $x^n$ where $n\neq-1$, so we can use the reverse power rule: $\int x^n\,dx=\dfrac{x^{n+1}}{n+1}+C$ $\begin{aligned} \int x^{{9}}\,dx&=\dfrac{x^{{9}+1}}{{9}+1}+C \\\\ &=\dfrac{1}{10} x^{10}+C \end{aligned}$ In conclusion, $\int x^{9}\,dx=\dfrac{1}{10} x^{10}+C$